50.9.6 problem 1(f)

Internal problem ID [7942]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number : 1(f)
Date solved : Monday, January 27, 2025 at 03:33:27 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+20 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)-9*diff(y(x),x)+20*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{4 x} c_{1} +{\mathrm e}^{5 x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]-9*D[y[x],x]+20*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{4 x} \left (c_2 e^x+c_1\right ) \]